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For the domain <math>S = I = \{ {}^{\backprime\backprime} \text{A} {}^{\prime\prime}, {}^{\backprime\backprime} \text{B} {}^{\prime\prime}, {}^{\backprime\backprime} \text{i} {}^{\prime\prime}, {}^{\backprime\backprime} \text{u} {}^{\prime\prime} \}\!</math> of four elements one needs to use four logical features, in effect, elevating each individual sign to the status of an exclusive grammatical category in its own right.  The easiest way to do this is simply to reuse the syntactic domain <math>S = I\!</math> as a logical alphabet <math>\underline{\underline{Y}},\!</math> taking element-wise identifications as follows:

For the domain <math>S = I = \{ {}^{\backprime\backprime} \text{A} {}^{\prime\prime}, {}^{\backprime\backprime} \text{B} {}^{\prime\prime}, {}^{\backprime\backprime} \text{i} {}^{\prime\prime}, {}^{\backprime\backprime} \text{u} {}^{\prime\prime} \}\!</math> of four elements one needs to use four logical features, in effect, elevating each individual sign to the status of an exclusive grammatical category in its own right.  The easiest way to do this is simply to reuse the syntactic domain <math>S = I\!</math> as a logical alphabet <math>\underline{\underline{Y}},\!</math> taking element-wise identifications as follows:

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Tables&nbsp;57.1, 57.2, and 57.3 show several ways of representing the elements of <math>O\!</math> and <math>S,\!</math> presenting the ''lateral'' codes for world elements in their ''mnemonic'', ''pragmatic'', and ''abstract'' versions, respectively.  In each Table, Column&nbsp;2 gives the coordinate vector <math>\underline{x} \in \underline{X}\!</math> or <math>\underline{y} \in \underline{Y}\!</math> as a bit string, using a subscript to indicate the relevant space, <math>\underline{X}\!</math> or <math>\underline{Y}.\!</math> Column&nbsp;3 lists the propositional expression of each element in the form of a conjunct term, in other words, as a logical product of positive and negative features, using doubly underlined capital letters for literal features of objects and doubly underlined lower case letters for literal features of quoted signs.  Finally, Column&nbsp;4 shows the compact code for each element, using a conjunction of positive features in subscripted angle brackets to represent the corresponding conjunct term as a singular proposition.

Tables 57.1, 57.2, and 57.3 show several ways of representing the elements of O and S, presenting the "lateral" codes for world elements in their "mnemonic", "pragmatic", and "abstract" versions, respectively.  In each Table, Column 2 gives the coordinate vector x C X or y C Y as a bit string, using a subscript to indicate the relevant space, X or Y.  Column 3 lists the propositional expression of each element in the form of a conjunct term, in other words, as a logical product of positive and negative features, using doubly underlined capital letters for literal features of objects and doubly underlined lower case letters for literal features of quoted signs.  Finally, Column 4 shows the compact code for each element, using a conjunction of positive features in subscripted angle brackets to represent the corresponding conjunct term as a singular proposition.

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